{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivatives Analytics with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**_Chapters 12 & 13_**\n",
    "\n",
    "**Wiley Finance (2015)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/images/derivatives_analytics_front.jpg\" alt=\"Derivatives Analytics with Python\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yves Hilpisch\n",
    "\n",
    "The Python Quants GmbH\n",
    "\n",
    "<a href='mailto:analytics@pythonquants.com'>analytics@pythonquants.com</a>\n",
    "\n",
    "<a href='http://pythonquants.com'>www.pythonquants.com</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 12: Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 270\n",
      "         Function evaluations: 485\n"
     ]
    }
   ],
   "source": [
    "%run 12_val/BCC97_simulation.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3225.930000, -0.000320, 0.146849, 0.104511, 0.175197])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array((S0, r0, kappa_r, theta_r, sigma_r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([22.211918, 0.024776, 0.952100, -0.999156, 0.036057, 0.008426,\n",
       "       -0.501069, 0.000000])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAEXCAYAAAAwdEdHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11902ebd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rate_paths(r)\n",
    "plt.savefig('../images/12_val/rate_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfsAAAEXCAYAAACqDe0rAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFRUVlQuc/w/rikSbqQRoJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11efc4ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_volatility_paths(v)\n",
    "plt.savefig('../images/12_val/volatility_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf4AAAEXCAYAAABMJCZvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n12g0Go1mBKGFX6PRaDSaEcT/B+ypm9oUKRJtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f052290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_index_paths(S)\n",
    "plt.savefig('../images/12_val/ES50_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgUAAAEXCAYAAAA9ajcAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4E6BmZmZJe4UmJmZGQD/D7QOuVWou9ZWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f379750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_index_histogram(S)\n",
    "plt.savefig('../images/12_val/ES50_histogram.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### European Options Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 12_val/BCC97_valuation_comparison.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 195.584 |   1.892\n",
      "  0.083 |   3225 |  62.147 |  64.162 |   2.016\n",
      "  0.083 |   3400 |   1.967 |   2.544 |   0.577\n",
      "  0.500 |   3050 | 259.126 | 272.960 |  13.834\n",
      "  0.500 |   3225 | 146.891 | 164.333 |  17.443\n",
      "  0.500 |   3400 |  67.142 |  85.330 |  18.188\n",
      "  1.000 |   3050 | 321.419 | 344.280 |  22.861\n",
      "  1.000 |   3225 | 216.227 | 243.415 |  27.188\n",
      "  1.000 |   3400 | 133.950 | 162.403 |  28.453\n",
      "  1.500 |   3050 | 378.978 | 407.035 |  28.057\n",
      "  1.500 |   3225 | 276.942 | 309.251 |  32.309\n",
      "  1.500 |   3400 | 193.333 | 227.887 |  34.554\n",
      "  2.000 |   3050 | 435.337 | 470.659 |  35.322\n",
      "  2.000 |   3225 | 335.010 | 374.315 |  39.305\n",
      "  2.000 |   3400 | 250.314 | 291.888 |  41.574\n",
      "  3.000 |   3050 | 549.127 | 594.413 |  45.287\n",
      "  3.000 |   3225 | 450.522 | 499.873 |  49.350\n",
      "  3.000 |   3400 | 364.049 | 416.300 |  52.252\n",
      "CPU times: user 16.2 s, sys: 1.59 s, total: 17.8 s\n",
      "Wall time: 6.13 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=50, I=50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 195.870 |   2.178\n",
      "  0.083 |   3225 |  62.147 |  64.609 |   2.462\n",
      "  0.083 |   3400 |   1.967 |   2.606 |   0.639\n",
      "  0.500 |   3050 | 259.126 | 273.046 |  13.920\n",
      "  0.500 |   3225 | 146.891 | 164.698 |  17.807\n",
      "  0.500 |   3400 |  67.142 |  85.852 |  18.710\n",
      "  1.000 |   3050 | 321.419 | 342.696 |  21.277\n",
      "  1.000 |   3225 | 216.227 | 241.375 |  25.148\n",
      "  1.000 |   3400 | 133.950 | 160.706 |  26.756\n",
      "  1.500 |   3050 | 378.978 | 407.341 |  28.363\n",
      "  1.500 |   3225 | 276.942 | 309.124 |  32.182\n",
      "  1.500 |   3400 | 193.333 | 227.473 |  34.140\n",
      "  2.000 |   3050 | 435.337 | 470.323 |  34.986\n",
      "  2.000 |   3225 | 335.010 | 373.940 |  38.930\n",
      "  2.000 |   3400 | 250.314 | 291.583 |  41.268\n",
      "  3.000 |   3050 | 549.127 | 597.571 |  48.444\n",
      "  3.000 |   3225 | 450.522 | 503.362 |  52.840\n",
      "  3.000 |   3400 | 364.049 | 420.019 |  55.970\n",
      "CPU times: user 55.3 s, sys: 7.28 s, total: 1min 2s\n",
      "Wall time: 26.7 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=50, I=200000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 193.241 |  -0.450\n",
      "  0.083 |   3225 |  62.147 |  61.595 |  -0.552\n",
      "  0.083 |   3400 |   1.967 |   2.581 |   0.614\n",
      "  0.500 |   3050 | 259.126 | 259.140 |   0.014\n",
      "  0.500 |   3225 | 146.891 | 149.090 |   2.199\n",
      "  0.500 |   3400 |  67.142 |  71.122 |   3.980\n",
      "  1.000 |   3050 | 321.419 | 322.117 |   0.697\n",
      "  1.000 |   3225 | 216.227 | 219.528 |   3.301\n",
      "  1.000 |   3400 | 133.950 | 139.285 |   5.335\n",
      "  1.500 |   3050 | 378.978 | 377.499 |  -1.479\n",
      "  1.500 |   3225 | 276.942 | 278.276 |   1.334\n",
      "  1.500 |   3400 | 193.333 | 197.137 |   3.804\n",
      "  2.000 |   3050 | 435.337 | 435.067 |  -0.270\n",
      "  2.000 |   3225 | 335.010 | 337.597 |   2.587\n",
      "  2.000 |   3400 | 250.314 | 255.541 |   5.227\n",
      "  3.000 |   3050 | 549.127 | 552.842 |   3.715\n",
      "  3.000 |   3225 | 450.522 | 457.774 |   7.252\n",
      "  3.000 |   3400 | 364.049 | 374.340 |  10.291\n",
      "CPU times: user 51.2 s, sys: 6.16 s, total: 57.4 s\n",
      "Wall time: 24.5 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=200, I=50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### American Options Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 12_val/BCC97_american_valuation.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      P0 |     LSM |    DIFF\n",
      "  0.083 |   3050 |  17.681 |  17.431 |  -0.250\n",
      "  0.083 |   3225 |  61.131 |  61.001 |  -0.130\n",
      "  0.083 |   3400 | 175.947 | 181.570 |   5.624\n",
      "  0.500 |   3050 |  77.963 |  84.277 |   6.314\n",
      "  0.500 |   3225 | 140.428 | 149.270 |   8.842\n",
      "  0.500 |   3400 | 235.379 | 246.148 |  10.769\n",
      "  1.000 |   3050 | 124.220 | 136.155 |  11.934\n",
      "  1.000 |   3225 | 192.808 | 207.958 |  15.149\n",
      "  1.000 |   3400 | 284.311 | 302.051 |  17.740\n",
      "  1.500 |   3050 | 155.970 | 174.854 |  18.884\n",
      "  1.500 |   3225 | 226.234 | 250.278 |  24.044\n",
      "  1.500 |   3400 | 314.923 | 344.215 |  29.292\n",
      "  2.000 |   3050 | 177.841 | 206.460 |  28.619\n",
      "  2.000 |   3225 | 247.834 | 282.910 |  35.077\n",
      "  2.000 |   3400 | 333.458 | 376.600 |  43.142\n",
      "  3.000 |   3050 | 201.032 | 249.858 |  48.826\n",
      "  3.000 |   3225 | 267.549 | 328.487 |  60.937\n",
      "  3.000 |   3400 | 346.197 | 421.464 |  75.267\n",
      "CPU times: user 1min 57s, sys: 10.4 s, total: 2min 8s\n",
      "Wall time: 40.5 s\n"
     ]
    }
   ],
   "source": [
    "%time lsm_compare_values(M0=150, I=50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 13: Dynamic Hedging"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BSM Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 13_dyh/BSM_lsm_hedging_algorithm.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "APPROXIMATION OF FIRST ORDER \n",
      "-----------------------------\n",
      "    step |     S_t |   Delta \n",
      "       1 |   34.97 |   -0.79\n",
      "       2 |   36.14 |   -0.70\n",
      "       3 |   36.40 |   -0.67\n",
      "       4 |   37.61 |   -0.59\n",
      "       5 |   37.41 |   -0.59\n",
      "          wrong\n",
      "       6 |   38.52 |   -0.54\n",
      "       7 |   39.43 |   -0.48\n",
      "       8 |   40.09 |   -0.43\n",
      "       9 |   40.07 |   -0.41\n",
      "          wrong\n",
      "      10 |   41.79 |   -0.32\n",
      "      11 |   41.26 |   -0.33\n",
      "      12 |   40.22 |   -0.38\n",
      "      13 |   38.42 |   -0.51\n",
      "      14 |   37.98 |   -0.57\n",
      "      15 |   36.79 |   -0.68\n",
      "      16 |   35.86 |   -0.78\n",
      "      17 |   34.49 |   -0.90\n",
      "      18 |   34.48 |   -0.90\n",
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BSM)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.995\n",
      "Bonds                40.303\n",
      "Cost                  4.474\n",
      "\n",
      "Regular Rehedges \n",
      "--------------------------------------------------------------------\n",
      "step|     S_t|    Port|     Put|    Diff|   Stock|    Bond|    Cost|\n",
      "   1|  34.968|   5.549|   5.215|   0.334|  -0.789|  33.156|   5.549|\n",
      "   2|  36.145|   4.660|   4.369|   0.291|  -0.700|  29.956|   4.660|\n",
      "   3|  36.398|   4.518|   4.181|   0.337|  -0.671|  28.926|   4.518|\n",
      "   4|  37.614|   3.738|   3.452|   0.286|  -0.590|  25.944|   3.738|\n",
      "   5|  37.415|   3.887|   3.550|   0.336|  -0.587|  25.833|   3.887|\n",
      "   6|  38.519|   3.270|   2.968|   0.301|  -0.538|  23.979|   3.270|\n",
      "   7|  39.430|   2.809|   2.539|   0.270|  -0.477|  21.624|   2.809|\n",
      "   8|  40.090|   2.520|   2.277|   0.243|  -0.434|  19.911|   2.520|\n",
      "   9|  40.071|   2.552|   2.267|   0.285|  -0.414|  19.153|   2.552|\n",
      "  10|  41.790|   1.863|   1.641|   0.221|  -0.322|  15.309|   1.863|\n",
      "  11|  41.262|   2.051|   1.830|   0.221|  -0.330|  15.666|   2.051|\n",
      "  12|  40.217|   2.415|   2.198|   0.217|  -0.376|  17.528|   2.415|\n",
      "  13|  38.419|   3.111|   3.026|   0.085|  -0.515|  22.880|   3.111|\n",
      "  14|  37.980|   3.365|   3.247|   0.118|  -0.569|  24.966|   3.365|\n",
      "  15|  36.795|   4.069|   3.959|   0.110|  -0.679|  29.062|   4.069|\n",
      "  16|  35.858|   4.740|   4.531|   0.209|  -0.778|  32.623|   4.740|\n",
      "  17|  34.488|   5.844|   5.616|   0.229|  -0.898|  36.805|   5.844|\n",
      "  18|  34.477|   5.899|   5.623|   0.276|  -0.905|  37.091|   5.899|\n",
      "MSE               0.061\n",
      "Average Error     0.230\n",
      "Total P&L         4.370\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BSM_hedge_run(p=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAGoCAYAAABL+58oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRffG1LkHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f0f0ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "# plt.savefig('../images/13_dyh/BSM_hedge_run_1.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "APPROXIMATION OF FIRST ORDER \n",
      "-----------------------------\n",
      "    step |     S_t |   Delta \n",
      "       1 |   35.31 |   -0.75\n",
      "       2 |   36.25 |   -0.69\n",
      "       3 |   37.50 |   -0.61\n",
      "       4 |   35.98 |   -0.69\n",
      "       5 |   36.52 |   -0.65\n",
      "       6 |   35.98 |   -0.70\n",
      "       7 |   35.55 |   -0.75\n",
      "       8 |   35.89 |   -0.72\n",
      "       9 |   38.18 |   -0.53\n",
      "      10 |   38.25 |   -0.52\n",
      "      11 |   38.00 |   -0.54\n",
      "      12 |   37.80 |   -0.56\n",
      "      13 |   39.22 |   -0.45\n",
      "      14 |   39.54 |   -0.44\n",
      "      15 |   39.82 |   -0.42\n",
      "      16 |   39.29 |   -0.46\n",
      "      17 |   38.11 |   -0.56\n",
      "      18 |   38.10 |   -0.57\n",
      "      19 |   39.61 |   -0.43\n",
      "      20 |   40.22 |   -0.39\n",
      "      21 |   39.78 |   -0.43\n",
      "      22 |   39.90 |   -0.42\n",
      "      23 |   39.82 |   -0.44\n",
      "      24 |   41.30 |   -0.32\n",
      "      25 |   42.60 |   -0.23\n",
      "      26 |   42.86 |   -0.21\n",
      "      27 |   44.64 |   -0.13\n",
      "      28 |   42.78 |   -0.22\n",
      "      29 |   42.22 |   -0.26\n",
      "      30 |   42.15 |   -0.27\n",
      "      31 |   41.36 |   -0.33\n",
      "      32 |   44.03 |   -0.14\n",
      "      33 |   45.28 |   -0.08\n",
      "      34 |   44.03 |   -0.14\n",
      "      35 |   43.86 |   -0.15\n",
      "      36 |   44.61 |   -0.10\n",
      "      37 |   46.20 |   -0.02\n",
      "      38 |   46.10 |   -0.02\n",
      "          wrong\n",
      "      39 |   44.46 |   -0.10\n",
      "      40 |   43.52 |   -0.15\n",
      "      41 |   42.29 |   -0.26\n",
      "      42 |   42.84 |   -0.21\n",
      "      43 |   41.33 |   -0.36\n",
      "      44 |   42.18 |   -0.27\n",
      "      45 |   41.95 |   -0.28\n",
      "      46 |   40.84 |   -0.41\n",
      "      47 |   40.71 |   -0.42\n",
      "      48 |   40.80 |   -0.42\n",
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BSM)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.995\n",
      "Bonds                40.303\n",
      "Cost                  4.474\n",
      "\n",
      "Regular Rehedges \n",
      "--------------------------------------------------------------------\n",
      "step|     S_t|    Port|     Put|    Diff|   Stock|    Bond|    Cost|\n",
      "   1|  35.308|   5.211|   4.945|   0.266|  -0.747|  31.602|   5.211|\n",
      "   2|  36.252|   4.543|   4.297|   0.246|  -0.692|  29.618|   4.543|\n",
      "   3|  37.503|   3.713|   3.500|   0.213|  -0.607|  26.487|   3.713|\n",
      "   4|  35.983|   4.668|   4.481|   0.187|  -0.690|  29.499|   4.668|\n",
      "   5|  36.517|   4.335|   4.089|   0.246|  -0.654|  28.211|   4.335|\n",
      "   6|  35.979|   4.720|   4.492|   0.228|  -0.703|  30.005|   4.720|\n",
      "   7|  35.548|   5.059|   4.817|   0.242|  -0.754|  31.880|   5.059|\n",
      "   8|  35.887|   4.842|   4.552|   0.290|  -0.715|  30.512|   4.842|\n",
      "   9|  38.183|   3.236|   3.134|   0.103|  -0.526|  23.311|   3.236|\n",
      "  10|  38.251|   3.229|   3.074|   0.154|  -0.518|  23.052|   3.229|\n",
      "  11|  38.001|   3.386|   3.257|   0.129|  -0.543|  24.017|   3.386|\n",
      "  12|  37.801|   3.523|   3.327|   0.196|  -0.563|  24.787|   3.523|\n",
      "  13|  39.224|   2.752|   2.637|   0.115|  -0.447|  20.296|   2.752|\n",
      "  14|  39.537|   2.637|   2.487|   0.150|  -0.445|  20.219|   2.637|\n",
      "  15|  39.821|   2.535|   2.377|   0.158|  -0.416|  19.091|   2.535|\n",
      "  16|  39.290|   2.779|   2.591|   0.187|  -0.460|  20.858|   2.779|\n",
      "  17|  38.107|   3.348|   3.171|   0.177|  -0.564|  24.859|   3.348|\n",
      "  18|  38.095|   3.385|   3.187|   0.198|  -0.567|  24.995|   3.385|\n",
      "  19|  39.614|   2.553|   2.456|   0.097|  -0.432|  19.653|   2.553|\n",
      "  20|  40.221|   2.315|   2.214|   0.101|  -0.392|  18.099|   2.315|\n",
      "  21|  39.775|   2.511|   2.394|   0.117|  -0.433|  19.733|   2.511|\n",
      "  22|  39.904|   2.479|   2.333|   0.147|  -0.424|  19.417|   2.479|\n",
      "  23|  39.821|   2.538|   2.361|   0.176|  -0.436|  19.895|   2.538|\n",
      "  24|  41.296|   1.919|   1.825|   0.094|  -0.318|  15.071|   1.919|\n",
      "  25|  42.603|   1.521|   1.431|   0.090|  -0.230|  11.316|   1.521|\n",
      "  26|  42.863|   1.474|   1.350|   0.124|  -0.208|  10.385|   1.474|\n",
      "  27|  44.637|   1.118|   0.962|   0.156|  -0.129|   6.894|   1.118|\n",
      "  28|  42.777|   1.367|   1.370|  -0.003|  -0.216|  10.598|   1.367|\n",
      "  29|  42.225|   1.499|   1.538|  -0.039|  -0.258|  12.386|   1.499|\n",
      "  30|  42.148|   1.533|   1.562|  -0.029|  -0.266|  12.750|   1.533|\n",
      "  31|  41.361|   1.758|   1.805|  -0.046|  -0.327|  15.284|   1.758|\n",
      "  32|  44.033|   0.903|   1.091|  -0.188|  -0.141|   7.114|   0.903|\n",
      "  33|  45.279|   0.736|   0.848|  -0.112|  -0.077|   4.225|   0.736|\n",
      "  34|  44.028|   0.837|   1.075|  -0.238|  -0.137|   6.880|   0.837|\n",
      "  35|  43.862|   0.868|   1.120|  -0.252|  -0.146|   7.279|   0.868|\n",
      "  36|  44.608|   0.768|   0.976|  -0.208|  -0.101|   5.283|   0.768|\n",
      "  37|  46.195|   0.614|   0.705|  -0.092|  -0.024|   1.740|   0.614|\n",
      "  38|  46.097|   0.618|   0.711|  -0.093|  -0.021|   1.605|   0.618|\n",
      "  39|  44.460|   0.655|   0.999|  -0.344|  -0.096|   4.941|   0.655|\n",
      "  40|  43.522|   0.751|   1.199|  -0.448|  -0.152|   7.363|   0.751|\n",
      "  41|  42.289|   0.948|   1.514|  -0.567|  -0.261|  11.966|   0.948|\n",
      "  42|  42.839|   0.819|   1.366|  -0.548|  -0.211|   9.871|   0.819|\n",
      "  43|  41.327|   1.150|   1.797|  -0.647|  -0.358|  15.932|   1.150|\n",
      "  44|  42.176|   0.865|   1.522|  -0.656|  -0.268|  12.158|   0.865|\n",
      "  45|  41.953|   0.940|   1.606|  -0.667|  -0.283|  12.819|   0.940|\n",
      "  46|  40.844|   1.269|   1.965|  -0.696|  -0.407|  17.911|   1.269|\n",
      "  47|  40.713|   1.344|   1.995|  -0.651|  -0.424|  18.590|   1.344|\n",
      "  48|  40.797|   1.331|   1.907|  -0.576|  -0.416|  18.300|   1.331|\n",
      "MSE               0.093\n",
      "Average Error    -0.051\n",
      "Total P&L        -2.511\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BSM_hedge_run(p=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAGoCAYAAABL+58oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSnBERESk6Px/2eOh4rfiwMoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b4f7150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "# plt.savefig('../images/13_dyh/BSM_hedge_run_2.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 13_dyh/BSM_lsm_hedging_histogram.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of American Put Option is    4.493\n",
      "Delta t=0 is                      -0.406\n",
      "run  1000   p/l    0.339\n",
      "run  2000   p/l   -0.067\n",
      "run  3000   p/l    0.379\n",
      "run  4000   p/l   -0.029\n",
      "run  5000   p/l    0.286\n",
      "run  6000   p/l    0.244\n",
      "run  7000   p/l   -0.761\n",
      "run  8000   p/l   -0.761\n",
      "run  9000   p/l   -0.002\n",
      "run 10000   p/l   -0.257\n",
      "\n",
      "SUMMARY STATISTICS FOR P&L\n",
      "---------------------------------\n",
      "Dynamic Replications        10000\n",
      "Time Steps                     50\n",
      "Paths for Valuation         10000\n",
      "Maximum                     5.447\n",
      "Average                     0.041\n",
      "Median                      0.036\n",
      "Minimum                   -11.475\n",
      "---------------------------------\n",
      "CPU times: user 8.34 s, sys: 351 ms, total: 8.69 s\n",
      "Wall time: 6.75 s\n"
     ]
    }
   ],
   "source": [
    "%time pl_list = BSM_dynamic_hedge_mcs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfsAAAF8CAYAAADIPhKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNntJkoqz2UuSVNz/B8Vk9w+LXeomAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b9934d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "plt.savefig('../images/13_dyh/BSM_hedge_histo.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of American Put Option is    4.471\n",
      "Delta t=0 is                      -1.028\n",
      "run  1000   p/l   -0.025\n",
      "run  2000   p/l    0.056\n",
      "run  3000   p/l    0.170\n",
      "run  4000   p/l    0.353\n",
      "run  5000   p/l   -0.014\n",
      "run  6000   p/l   -0.208\n",
      "run  7000   p/l   -0.124\n",
      "run  8000   p/l   -0.359\n",
      "run  9000   p/l   -0.030\n",
      "run 10000   p/l   -0.008\n",
      "\n",
      "SUMMARY STATISTICS FOR P&L\n",
      "---------------------------------\n",
      "Dynamic Replications        10000\n",
      "Time Steps                    200\n",
      "Paths for Valuation        150000\n",
      "Maximum                     2.134\n",
      "Average                     0.004\n",
      "Median                      0.016\n",
      "Minimum                    -1.323\n",
      "---------------------------------\n",
      "CPU times: user 1min 27s, sys: 5.07 s, total: 1min 32s\n",
      "Wall time: 42.9 s\n"
     ]
    }
   ],
   "source": [
    "%time pl_list = BSM_dynamic_hedge_mcs(M=200, I=150000) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfkAAAF8CAYAAADMy8KPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUtQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f71c3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "# plt.savefig('../images/13_dyh/BSM_hedge_histo_more.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BCC97 Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 13_dyh/BCC97_lsm_hedging_algorithm.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BCC97)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.426\n",
      "Bonds              1602.498\n",
      "Cost                228.305\n",
      "\n",
      "Regular Rehedges \n",
      "----------------------------------------------------------------------------------\n",
      "step|       S_t|      Port|       Put|      Diff|     Stock|      Bond|      Cost|\n",
      "   1|  3293.090|   199.691|   201.600|    -1.909|    -1.856|  6311.671|   199.691|\n",
      "   2|  3323.629|   143.027|   186.740|   -43.712|    -0.318|  1201.164|   143.027|\n",
      "   3|  3352.073|   133.986|   175.533|   -41.547|    -0.358|  1335.492|   133.986|\n",
      "   4|  3380.280|   123.907|   163.659|   -39.752|    -0.429|  1572.799|   123.907|\n",
      "   5|  3370.652|   128.084|   165.605|   -37.521|    -0.401|  1481.094|   128.084|\n",
      "   6|  3398.985|   116.788|   153.569|   -36.781|    -0.381|  1410.163|   116.788|\n",
      "   7|  3369.633|   128.053|   160.805|   -32.752|    -0.408|  1503.294|   128.053|\n",
      "   8|  3289.659|   160.744|   187.601|   -26.858|    -0.437|  1598.083|   160.744|\n",
      "   9|  3286.331|   162.201|   184.473|   -22.272|    -0.472|  1714.368|   162.201|\n",
      "  10|  3072.690|   263.123|   284.850|   -21.728|    -0.615|  2153.371|   263.123|\n",
      "  11|  3062.960|   269.162|   286.396|   -17.234|    -0.620|  2169.351|   269.162|\n",
      "  12|  3089.016|   253.057|   269.050|   -15.993|    -0.586|  2062.950|   253.057|\n",
      "  13|  3131.731|   228.088|   244.894|   -16.806|    -0.605|  2122.716|   228.088|\n",
      "  14|  2919.759|   356.410|   374.043|   -17.633|    -0.719|  2456.331|   356.410|\n",
      "  15|  2924.716|   352.992|   368.183|   -15.190|    -0.715|  2445.309|   352.992|\n",
      "  16|  2985.576|   309.674|   324.159|   -14.485|    -0.674|  2322.644|   309.674|\n",
      "  17|  3010.488|   293.137|   305.393|   -12.257|    -0.671|  2312.873|   293.137|\n",
      "  18|  3035.974|   276.272|   286.501|   -10.229|    -0.664|  2291.587|   276.272|\n",
      "  19|  2969.817|   320.364|   328.543|    -8.179|    -0.717|  2450.217|   320.364|\n",
      "  20|  2955.277|   330.957|   336.499|    -5.543|    -0.730|  2488.901|   330.957|\n",
      "  21|  2910.463|   363.812|   367.966|    -4.154|    -0.775|  2619.850|   363.812|\n",
      "  22|  2936.027|   344.124|   347.962|    -3.838|    -0.763|  2585.737|   344.124|\n",
      "  23|  2987.578|   304.899|   306.569|    -1.671|    -0.743|  2525.017|   304.899|\n",
      "  24|  3041.506|   264.946|   268.346|    -3.400|    -0.724|  2466.747|   264.946|\n",
      "  25|  3066.863|   246.702|   248.523|    -1.820|    -0.713|  2433.393|   246.702|\n",
      "  26|  3085.940|   233.253|   234.646|    -1.393|    -0.731|  2489.226|   233.253|\n",
      "  27|  2942.050|   338.668|   331.666|     7.002|    -0.807|  2712.051|   338.668|\n",
      "  28|  3004.776|   288.394|   282.345|     6.049|    -0.784|  2644.029|   288.394|\n",
      "  29|  2970.714|   315.412|   304.893|    10.519|    -0.800|  2693.090|   315.412|\n",
      "  30|  2925.292|   352.084|   340.969|    11.115|    -0.834|  2792.550|   352.084|\n",
      "  31|  2950.434|   331.659|   316.799|    14.860|    -0.825|  2764.770|   331.659|\n",
      "  32|  2975.783|   311.372|   293.654|    17.718|    -0.817|  2742.629|   311.372|\n",
      "  33|  3000.930|   291.387|   270.351|    21.036|    -0.824|  2765.407|   291.387|\n",
      "  34|  3026.450|   271.055|   249.040|    22.015|    -0.835|  2799.472|   271.055|\n",
      "  35|  3052.321|   250.229|   226.402|    23.827|    -0.846|  2831.893|   250.229|\n",
      "  36|  3040.977|   260.583|   232.051|    28.531|    -0.865|  2890.750|   260.583|\n",
      "  37|  2944.367|   344.821|   312.481|    32.340|    -0.891|  2968.693|   344.821|\n",
      "  38|  2969.569|   323.101|   286.949|    36.151|    -0.885|  2950.267|   323.101|\n",
      "  39|  3063.118|   241.251|   203.197|    38.053|    -0.878|  2931.744|   241.251|\n",
      "  40|  3086.580|   221.609|   182.630|    38.979|    -0.890|  2967.876|   221.609|\n",
      "  41|  3120.600|   192.468|   154.231|    38.237|    -0.899|  2998.923|   192.468|\n",
      "  42|  3087.541|   223.555|   173.331|    50.224|    -0.921|  3067.014|   223.555|\n",
      "  43|  3114.275|   200.330|   148.137|    52.193|    -0.922|  3072.192|   200.330|\n",
      "  44|  3171.573|   148.889|   105.082|    43.807|    -0.925|  3083.025|   148.889|\n",
      "  45|  3216.916|   108.229|    75.952|    32.278|    -0.931|  3102.564|   108.229|\n",
      "  46|  3089.488|   228.041|   152.105|    75.936|    -0.949|  3159.463|   228.041|\n",
      "  47|  2993.663|   320.436|   241.184|    79.252|    -0.964|  3205.245|   320.436|\n",
      "  48|  2852.621|   457.738|   377.569|    80.168|    -0.973|  3233.375|   457.738|\n",
      "  49|  2931.133|   382.376|   295.071|    87.305|    -0.990|  3283.929|   382.376|\n",
      "  50|  2872.067|   441.749|   353.863|    87.886|     0.000|  3283.929|  3283.929|\n",
      "MSE             1268.786\n",
      "Average Error     9.428\n",
      "Total P&L       480.826\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAGoCAYAAABL+58oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f32d850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_1.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BCC97)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.426\n",
      "Bonds              1602.498\n",
      "Cost                228.305\n",
      "\n",
      "Regular Rehedges \n",
      "----------------------------------------------------------------------------------\n",
      "step|       S_t|      Port|       Put|      Diff|     Stock|      Bond|      Cost|\n",
      "   1|  3313.460|   191.013|   193.940|    -2.927|    -1.821|  6224.627|   191.013|\n",
      "   2|  3358.312|   109.360|   174.333|   -64.973|    -0.312|  1158.262|   109.360|\n",
      "   3|  3387.038|   100.396|   163.691|   -63.295|    -0.348|  1278.376|   100.396|\n",
      "   4|  3446.356|    79.780|   143.499|   -63.719|    -0.333|  1226.302|    79.780|\n",
      "   5|  3505.434|    60.134|   125.819|   -65.685|    -0.287|  1066.504|    60.134|\n",
      "   6|  3451.654|    75.581|   138.349|   -62.768|    -0.326|  1201.991|    75.581|\n",
      "   7|  3424.400|    84.498|   144.092|   -59.594|    -0.379|  1381.102|    84.498|\n",
      "   8|  3452.853|    73.764|   133.176|   -59.413|    -0.341|  1249.590|    73.764|\n",
      "   9|  3480.874|    64.261|   123.064|   -58.802|    -0.347|  1270.859|    64.261|\n",
      "  10|  3510.073|    54.169|   113.630|   -59.461|    -0.323|  1188.855|    54.169|\n",
      "  11|  3542.419|    43.737|   104.876|   -61.139|    -0.335|  1230.183|    43.737|\n",
      "  12|  3575.594|    32.667|    94.981|   -62.314|    -0.336|  1233.738|    32.667|\n",
      "  13|  3458.420|    72.072|   119.671|   -47.599|    -0.440|  1592.216|    72.072|\n",
      "  14|  3498.503|    54.487|   106.878|   -52.391|    -0.436|  1579.494|    54.487|\n",
      "  15|  3547.467|    33.167|    93.118|   -59.951|    -0.394|  1430.149|    33.167|\n",
      "  16|  3321.288|   122.270|   153.917|   -31.648|    -0.507|  1805.186|   122.270|\n",
      "  17|  3360.778|   102.331|   138.308|   -35.977|    -0.505|  1798.837|   102.331|\n",
      "  18|  3351.218|   107.277|   139.169|   -31.892|    -0.520|  1850.249|   107.277|\n",
      "  19|  3413.640|    74.998|   118.217|   -43.219|    -0.509|  1811.857|    74.998|\n",
      "  20|  3131.560|   218.706|   226.652|    -7.946|    -0.658|  2279.922|   218.706|\n",
      "  21|  3172.123|   192.151|   204.175|   -12.024|    -0.670|  2318.206|   192.151|\n",
      "  22|  3230.686|   153.052|   173.419|   -20.367|    -0.644|  2235.011|   153.052|\n",
      "  23|  3279.892|   121.530|   149.290|   -27.760|    -0.627|  2177.177|   121.530|\n",
      "  24|  3327.516|    91.845|   129.861|   -38.015|    -0.615|  2137.967|    91.845|\n",
      "  25|  3335.272|    87.252|   123.984|   -36.732|    -0.625|  2172.617|    87.252|\n",
      "  26|  3392.194|    51.924|   102.470|   -50.546|    -0.533|  1858.647|    51.924|\n",
      "  27|  3448.947|    21.930|    85.855|   -63.925|     0.000|    21.930|    21.930|\n",
      "  28|  3443.132|    21.932|    84.257|   -62.326|     0.000|    21.932|    21.932|\n",
      "  29|  3433.804|    21.933|    82.633|   -60.701|    -0.011|    58.808|    21.933|\n",
      "  30|  3415.413|    22.136|    85.060|   -62.924|    -0.107|   387.099|    22.136|\n",
      "  31|  3482.287|    15.038|    65.801|   -50.763|     0.000|    15.038|    15.038|\n",
      "  32|  3525.497|    15.041|    55.130|   -40.089|     0.000|    15.041|    15.041|\n",
      "  33|  3401.448|    15.044|    76.888|   -61.845|    -0.128|   450.668|    15.044|\n",
      "  34|  3316.261|    26.031|    98.885|   -72.854|    -0.780|  2612.795|    26.031|\n",
      "  35|  3379.226|   -22.575|    76.007|   -98.582|     0.000|   -22.575|   -22.575|\n",
      "  36|  3390.924|   -22.580|    69.196|   -91.776|     0.000|   -22.580|   -22.580|\n",
      "  37|  3453.876|   -22.584|    52.018|   -74.601|     0.000|   -22.584|   -22.584|\n",
      "  38|  3483.156|   -22.587|    41.942|   -64.529|     0.000|   -22.587|   -22.587|\n",
      "  39|  3499.450|   -22.592|    37.892|   -60.484|     0.000|   -22.592|   -22.592|\n",
      "  40|  3470.900|   -22.597|    38.196|   -60.793|     0.000|   -22.597|   -22.597|\n",
      "  41|  3486.621|   -22.603|    32.174|   -54.777|     0.000|   -22.603|   -22.603|\n",
      "  42|  3498.130|   -22.610|    27.045|   -49.655|     0.000|   -22.610|   -22.610|\n",
      "  43|  3521.859|   -22.617|    20.986|   -43.603|     0.000|   -22.617|   -22.617|\n",
      "  44|  3447.254|   -22.624|    24.823|   -47.447|     0.000|   -22.624|   -22.624|\n",
      "  45|  3448.858|   -22.631|    20.702|   -43.333|     0.000|   -22.631|   -22.631|\n",
      "  46|  3525.608|   -22.639|    10.306|   -32.945|     0.000|   -22.639|   -22.639|\n",
      "  47|  3585.029|   -22.648|     4.702|   -27.350|     0.000|   -22.648|   -22.648|\n",
      "  48|  3598.532|   -22.658|     2.043|   -24.701|     0.000|   -22.658|   -22.658|\n",
      "  49|  3640.963|   -22.666|     0.337|   -23.003|     0.000|   -22.666|   -22.666|\n",
      "  50|  3638.397|   -22.674|     0.000|   -22.674|     0.000|   -22.666|   -22.666|\n",
      "MSE             2782.617\n",
      "Average Error   -48.546\n",
      "Total P&L       -2475.835\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAGoCAYAAABL+58oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiISM1RgCMiIiI1RwGOiIiI1Jz/D/u/gB7nCq0BAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f080ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t + 1)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_2.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "DYNAMIC HEDGING OF AMERICAN PUT (BCC97)\n",
      "---------------------------------------\n",
      "Initial Hedge\n",
      "Stocks               -0.426\n",
      "Bonds              1602.498\n",
      "Cost                228.305\n",
      "\n",
      "Regular Rehedges \n",
      "----------------------------------------------------------------------------------\n",
      "step|       S_t|      Port|       Put|      Diff|     Stock|      Bond|      Cost|\n",
      "   1|  3334.785|   181.929|   186.347|    -4.418|    -1.787|  6140.884|   181.929|\n",
      "   2|  3308.847|   228.296|   192.136|    36.160|    -0.353|  1397.161|   228.296|\n",
      "   3|  3257.391|   246.484|   210.867|    35.617|    -0.450|  1713.090|   246.484|\n",
      "   4|  3284.768|   234.181|   197.179|    37.002|    -0.426|  1631.876|   234.181|\n",
      "   5|  3399.651|   185.310|   156.171|    29.138|    -0.350|  1375.014|   185.310|\n",
      "   6|  3285.852|   225.136|   192.522|    32.614|    -0.425|  1620.463|   225.136|\n",
      "   7|  3351.304|   197.344|   166.841|    30.503|    -0.411|  1575.848|   197.344|\n",
      "   8|  3408.658|   173.758|   146.445|    27.312|    -0.361|  1405.020|   173.758|\n",
      "   9|  3432.936|   165.000|   136.218|    28.782|    -0.377|  1459.126|   165.000|\n",
      "  10|  3464.136|   153.260|   125.774|    27.486|    -0.356|  1387.360|   153.260|\n",
      "  11|  3525.190|   131.523|   108.899|    22.624|    -0.349|  1361.624|   131.523|\n",
      "  12|  3536.579|   127.551|   103.206|    24.345|    -0.355|  1384.215|   127.551|\n",
      "  13|  3522.552|   132.539|   103.601|    28.938|    -0.407|  1565.208|   132.539|\n",
      "  14|  3380.873|   190.176|   139.879|    50.297|    -0.489|  1844.271|   190.176|\n",
      "  15|  3348.353|   206.117|   146.822|    59.295|    -0.505|  1898.623|   206.117|\n",
      "  16|  3376.015|   192.176|   135.674|    56.503|    -0.455|  1729.234|   192.176|\n",
      "  17|  3443.098|   161.704|   114.267|    47.437|    -0.452|  1719.386|   161.704|\n",
      "  18|  3502.142|   135.088|    97.583|    37.505|    -0.429|  1639.101|   135.088|\n",
      "  19|  3539.960|   118.978|    87.569|    31.410|    -0.136|   600.342|   118.978|\n",
      "  20|  3595.655|   111.474|    73.819|    37.655|     0.000|   111.474|   111.474|\n",
      "  21|  3465.029|   111.490|    99.232|    12.258|    -0.521|  1915.697|   111.490|\n",
      "  22|  3510.036|    88.437|    85.421|     3.016|    -0.085|   387.739|    88.437|\n",
      "  23|  3574.016|    83.055|    70.160|    12.895|     0.000|    83.055|    83.055|\n",
      "  24|  3629.452|    83.070|    58.995|    24.075|     0.000|    83.070|    83.070|\n",
      "  25|  3514.418|    83.088|    76.891|     6.198|     0.000|    83.088|    83.088|\n",
      "  26|  3452.003|    83.109|    86.759|    -3.650|    -0.394|  1442.071|    83.109|\n",
      "  27|  3470.424|    76.250|    80.896|    -4.646|     0.000|    76.250|    76.250|\n",
      "  28|  3424.919|    76.275|    88.759|   -12.484|    -0.318|  1165.544|    76.275|\n",
      "  29|  3421.872|    77.658|    85.516|    -7.858|    -0.158|   619.007|    77.658|\n",
      "  30|  3145.398|   121.602|   188.305|   -66.703|    -0.787|  2596.273|   121.602|\n",
      "  31|  3043.384|   202.719|   246.126|   -43.407|    -0.806|  2657.092|   202.719|\n",
      "MSE             730.418\n",
      "Average Error    10.551\n",
      "Total P&L       538.086\n"
     ]
    }
   ],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAGoCAYAAABL+58oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHBEREak6SnBERESk6vx/DSXAnUlsyEwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119388410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t + 1)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_3.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 13_dyh/BCC97_lsm_hedging_histogram.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run  1000   p/l   33.596\n",
      "run  2000   p/l   -2.115\n",
      "run  3000   p/l  -17.951\n",
      "run  4000   p/l    2.579\n",
      "run  5000   p/l  -35.642\n",
      "run  6000   p/l  -16.109\n",
      "run  7000   p/l   26.780\n",
      "run  8000   p/l   14.318\n",
      "run  9000   p/l -506.078\n",
      "run 10000   p/l   45.902\n",
      "\n",
      "SUMMARY STATISTICS FOR P&L\n",
      "---------------------------------\n",
      "Dynamic Replications        10000\n",
      "Time Steps                    150\n",
      "Paths for Valuation        150000\n",
      "Maximum                   143.354\n",
      "Average                     4.343\n",
      "Median                     15.136\n",
      "Minimum                 -1014.275\n",
      "---------------------------------\n",
      "CPU times: user 1min 40s, sys: 13.2 s, total: 1min 53s\n",
      "Wall time: 59 s\n"
     ]
    }
   ],
   "source": [
    "%time pl_list = BCC97_hedge_simulation(M=150, I=150000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgEAAAF8CAYAAABWsmjjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIqZRMgSVKl/j8an8f8f3KyvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x101a95290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_histo.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://www.pythonquants.com\" target=\"_blank\">www.pythonquants.com</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a>\n",
    "\n",
    "<a href=\"mailto:analytics@pythonquants.com\">analytics@pythonquants.com</a>\n",
    "\n",
    "**Python Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://www.derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
